Session NO04: MFE: Turbulence and Transport

Exploring Experimental Isotope Scaling in Tokamak Transport*

A problem that has not yet been resolved is the scaling of tokamak transport with the ion mass¹. Candidates for explaining this scaling are mainly related to zonal flows². Such flows are central to both the understanding of the nonlinear Dimits shift and the H-mode barrier.  We note that zonal flows are sensitive to the fluid closure and also to the contribution to the Reynolds stress by the pressure.  We will study this effect in detail using our most general electromagnetic description,³ including kinetic ballooning modes as well as peeling modes and collisions. We will also compare this with the effects of fast particles since we have recently combined a theory for fast particles with our usual drift wave model⁴. In particular, it was found in Ref 2 that the effects of collisions may be needed for obtaining the experimental isotope scaling. We expect that collisions may be needed in the outer parts of the H-mode barrier, where our model is usually in the second stability region for MHD ballooning modes.

[1] J.W. Connor and H.R. Wilson, Plasma Phys. Control. Fusion 36, 719 (1994).

[2] S-I- Itoh and K. Itoh, Nuclear Fusion 56, 106028 (2016).

[3] J. Weiland, Stability and Transport in Magnetic Confinement Systems, Springer, New York (2012).

[4] J. Weiland, T. Rafiq and E. Shuster Phys. Plasmas 30, 042517 (2023).   

Nonlinear global simulations of microtearing transport in the pedestal

A thorough understanding of which processes set the residual turbulent transport in the pedestal region is a crucial step in determining the pedestal formation and its evolution. Recent linear gyrokinetic modeling indicates that Micro Tearing Modes (MTMs) reproduce key experimental features observed in several H-mode DIII-D pedestals. There are however no nonlinear simulations confirming these results due to the challenges associated with performing such runs.

We will present the first global nonlinear electromagnetic simulations (performed with the GENE code) of a DIII-D Elmy-H mode pedestal where, well within experimental error bars, the nonlinear electron heat transport is dominated at the ion scale by MTMs. Numerical results favorably compare with the experimental power balance as well as measured magnetic spectrograms. Electron scale contributions from ETG modes, also modeled with global gyrokinetic simulations, have a non-negligible contribution, suggesting that in the analyzed pedestal electron heat transport is regulated by a competition between these two transport mechanisms. Ion transport, in agreement with previous analysis, is dominated by neoclassical processes.

The kinetic ballooning limit is probed by varying the plasma profiles and plasma β , using both local and global simulations to assess the impact of the simulation model on the KBM threshold.   

Role of isotopes in microturbulence from linear to saturated Ohmic confinement regimes

The first principle gyrokinetic numerical experiments investigating the isotopic dependence of energy confinement achieve a quantitative agreement with experimental empirical scalings, particularly in Ohmic and L-mode tokamak plasmas. Mitigation of turbulence radial electric field intensity  and associated poloidal  fluctuating velocity with the radial correlation length  strongly deviating from the gyro-Bohm scaling is identified as the principal mechanism behind the isotope effects. Three primary contributors are classified, the deviation from gyro-Bohm scaling, zonal flow and trapped electron turbulence stabilization. Zonal flow enhances isotope effects primarily through reinforcing the inverse dependence of turbulence decorrelation rate on isotope mass with , which markedly differs from the characteristic linear frequency. The findings offer new insights into isotope effects, providing critical implications for energy confinement optimization in tokamak plasmas.   

Observation of L-mode-like core electron temperature fluctuations in H-mode plasmas at ASDEX Upgrade

Turbulence suppression is important to achieve enhanced confinement in tokamak plasmas. The Correlation Electron Cyclotron Emission (CECE) diagnostic measures turbulent electron temperature fluctuations (dTe/Te) important for transport. Prior work at DIII-D using CECE showed a large reduction in core (r/a ≈ 0.7) dTe/Te from L-mode (dTe/Te ≈ 1.3%) to H-mode (dTe/Te ≤ 0.33%) [1]. Using a new turbulence database [2], we observe significant temperature fluctuations (dTe/Te ≥ 1%) in the core (r/a ≈ 0.4) of auxiliary-heated ELMy H-modes in AUG. These results indicate that reduced core dTe/Te are not guaranteed during H-mode operation. Further, the dTe/Te appear to undergo an abrupt change in magnitude at a collisionality similar to that of Linear to Saturated Ohmic Confinement (LOC-SOC) transitions in ohmically-heated L-mode plasmas at AUG [3]. These results suggest that changes in turbulence underlying the LOC-SOC transition are not unique to ohmically-heated L-mode plasmas.

[1] L. Schmitz et al 2009 Nucl. Fusion 49 095004

[2] C. Yoo et al EPJ Web of Conferences 277, 03001 (2023)

[3] C. Angioni et al PRL 107, 215003 (2011)   

Zonal Flows in ADITYA-U tokamak

Plasma turbulence is known to be one of the strong driving mechanisms of energy and particle transport degrading the plasma confinement in tokamaks. Hence, it is important to understand different physical processes which drive and control turbulence. It has been observed that the self-generated axis-symmetric structures such as zonal flows play a key role in controlling the turbulence and associated transport². Low-frequency zonal flows (LFZF) and high-frequency geodesic acoustic mode (GAM)^2,4 have been observed and studied in several toroidal devices, However, several features related to the nature of these modes are still not fully understood. LFZF and GAM have been studied in ADITYA-U tokamak using poloidaly and toroidally distributed Langmuir probe arrays. Detailed analysis of density and floating potential fluctuations revealed the presence of LFZFs and GAM-like modes in typical ADITYA-U discharges. It has been observed that although the LFZFs are electrostatic, the GAM-like modes are triggered in high MHD activity plasma discharges of ADITYA-U tokamak. Magnetic oscillations (m/n=2/1) above a threshold of 3 G drive a similar frequency oscillation in the edge floating potential and ion saturation current fluctuations exciting a GAM-like mode with m/n=2/1 for floating potential and m/n=1/1 for ion saturation current fluctuation. A radial electric field in order of 1-3 kV/m up to a length scale in order of 1 cm, can be observed outside the magnetic island. When the magnetic island grows in size up to 5-6 cm, this radial electric field modifies the edge dynamics. This explains the existence of a threshold in magnetic fluctuation’s amplitude for this coupling to trigger. The radial electric field fluctuation induces a similar mode structure in floating potential and poloidal velocity fluctuation causes a GAM-like structure in density fluctuation. The excitation of this GAM-like mode coincides with a decrease in broadband turbulence, associated transport, and an increase in confinement. The complete analysis of LFZFs and GAM-like modes in ADITYA-U plasma will be presented in this paper.   

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While the low-to-High mode (L-H) transition and Edge localized modes have been described from a deterministic view point, their dynamics can fundamentally be affected by stochastic noises. In this talk, I will report such novel effects of stochastic noises on the dynamics of the L-H transition and ELMs by using a non-perturbative statistical theory. First, I will show how a stochastic noise can facilitate the transitions to the self-regulatory oscillatory (dithering) phase and the H-mode as well as leading to a mixed dithering-H-mode state. Furthermore, it will be shown that a probability density function (PDF) changes in time over the L-H transition and can be strongly non-Gaussian; intermittent zonal flows can appear and play an important role in regulating turbulence in the transitions. Second, I will discuss the effects of stochastic particle and magnetic perturbations on ELM suppression and mitigation via phase mixing. Furthermore, it will be shown that stochastic noises can significantly reduce power and energy losses caused by ELMs and reproduce the observed experimental scaling relation of the ELM power loss with the input power.    

Validity of using heat pulse diffusivity as a proxy for incremental diffusivity in validation studies

One metric which can be compared between plasma physics models and experiments in validation work is the incremental diffusivity, χ_e^inc(Creely et al., 2016). However, the quantity which can be experimentally measured is actually the heat pulse diffusivity, χ_e^HP­. In past work, the effective diffusivity, χ_e^eff, is assumed to be independent of the ion temperature gradient, ∇T_i, when proving equivalence between the incremental diffusivity, χ_e^inc, and the heat pulse diffusivity, χ_e^HP(Tubbing et al., 1987).   However, we expect that in strongly driven ITG transport, the electron heat transport would be sensitive to ion temperature gradients. Here, we use the ASTRA power balance code (Pereverzev et al., 1991) with TGLF SAT2 (Staebler et al., 2021) to test whether the heat pulse diffusivity, χ_e^HP, changes depending on whether or not we hold ∇T_i fixed. We explore which plasma conditions cause a discrepancy between the calculation of the heat pulse diffusivity, χ_e^HP, and the incremental diffusivity, χ_e^inc, suggesting that validation utilizing their comparison should be avoided in these regimes.   

Gyrokinetic analysis of General Fusion’s Magnetized Target Fusion (MTF) Plasmas

General Fusion (GF) is developing a Magnetized Target Fusion concept toward commercial fusion power production [1]. In MTF, a spherical tokamak target plasma is formed by coaxial helicity injection into a liquid metal flux conserver and compressed rapidly to reach fusion-relevant conditions. Pi3 at GF is a non-compressing device with solid lithium walls used to improve MTF targets to design future machines.  In this work, we present the first thermal transport analysis of Pi3 plasmas using gyrokinetic simulations. Local gyrokinetic flux tube simulations are performed for Pi3 shot 18669 in the radial range r/a=0.2-0.8, with reduced quasilinear code TGLF [2] to simulate turbulence and NEO [3] to simulate neoclassical transport. These simulations indicate that ITG and TEM modes are the most unstable modes in the ion-scale range, with no electron scale ETG modes for r/a<0.3. However, for 0.3<r/a<0.8, ETG unstable modes are present. The dominant transport channels for turbulent heat losses are ITG and TEM modes at small wavenumber. Transport is neoclassical for r/a<0.2, and anomalous for r/a>0.2. The future goal of this work is to perform sensitivity analysis concerning plasma profiles and validate quasilinear TGLF fluxes with nonlinear gyrokinetic code CGYRO for GF plasma conditions.  

 

[1] M. Laberge, JFE 38, 199203 (2019)

[2] G.M. Staebler  et al., POP 14, 055909 (2007)

[3] E. A. Belli and J. Candy, PPCF 50, 095010 (2008)   

Excitation of ion Bernstein wave (IBW) turbulence in nonlinear ITG simulations

This work presents a first of a kind simulation of IBW turbulence in the presence of temperature and density gradients, where the Larmor-frequency-scale waves are destabilized and have a significant contribution to the turbulent transport (comparable to ITG modes). Together with the analytical derivation of stability criteria for the IBW instability,  the simulations demonstrate that the focus on gyrokinetic simulations for the edge of a fusion device is not sufficient for developing a comprehensive understanding and that simulations with more complete models are necessary.

In regimes with high gradients and large turbulence fluctuations, such as the plasma edge of a fusion device, the limitations of gyrokinetic models become apparent. While gyrokinetic transport simulations are effective in the tokamak core regime, their applicability in high-gradient regimes is questionable. More comprehensive simulations are necessary to develop a deeper understanding of the dynamics in these regions.

The newly developed semi-Lagrangian solver for the 6D kinetic Vlasov system is based on a highly efficient scheme to treat the vxB-acceleration from the strong background magnetic field. The Lagrangian treatment of the Lorentz force advection allows the simulation of excitation and the resulting turbulence of waves far beyond the gyrokinetic regime.   

Development of a Lagrangian Gyrocenter Tracking Code (LGT1) for Application to CGYRO Calculated Turbulence

A Lagrangian Gyrocenter Tracking code (LGT1) is developed for evaluation of the Lagrangian correlation function (L_c) and Lagrangian diffusion coefficient (D_L) of the turbulence. The saturated turbulence fields (φ, A_||), used in LGT1, are calculated in advance with the nonlinear Eulerian gyrokinetic code CGYRO[1]. The Lagrangian correlations are a crucial part in the theory of transport. However, due to the Eulerian nature of CGYRO they are not directly calculable. LGT1 provides the further calculations needed to access the Lagrangian statistics. In LGT1 an ensemble of test particles (currently ions) is launched into the evolving turbulence fields (from CGYRO). For compatibilty with CGYRO and simplifying the calculations, field-aligned coordinates are employed for tracking the gyrocentrers. The ensemble of particles is initiated with velocities taken from a Maxwellian distribution. Further, particles are launched on the outboard midplane, with initial radial and binormal locations chosen randomly from the simulation box, for maximum sampling of turbulence. Particle drift velocities are then used for the evaluation of L_c and D_L. Future developments will include adding collision models and different particle species.

[1] J. Candy, E.A. Belli, and R.V. Bravenec. A high-accuracy Eulerian gyrokinetic solver for collisional plasmas. J. Comput. Phys., 324:73, 2016   

Nearly-integrable flows and chaotic tangles in the Dimits shift regime of plasma edge turbulence

Turbulent flows frequently exhibit spatiotemporal intermittency, reflecting a complex interplay between driving forces, dissipation, and transport. This intermittency often manifests as observable structures and patterns in the flow, introducing nontrivial statistical correlations that are challenging to understand and model. In this work, we use dynamical systems techniques to study the Dimits shift regime of the flux-balanced Hasegawa-Wakatani (BHW) equations, which models a transitional regime of resistive drift-wave turbulence. We show in direct numerical simulations that turbulence in this regime is dominated by strong zonal flows and coherent drift-wave vortex structures which maintain a strong linear character despite their large amplitude. Using the framework of generalized Liouville integrability, we develop a theory of integrable Lagrangian flows in generic fluid and plasma systems and discuss how the zonal flows plus drift waves exhibit a form of "near-integrability" originating from a fluid element relabeling symmetry. We further demonstrate that the BHW flows transition from integrability to chaos via the formation of chaotic tangles in the aperiodic Lagrangian flow, and establish a direct link between the 'lobes' associated with these tangles and intermittency in the turbulence statistics. This illustrates how studying the convective nonlinearity with dynamical systems theory can explain aspects of spatiotemporal intermittency in complex turbulent flows.   

Global gyrokinetic simulations of the impact of magnetic island on ion temperature gradient driven turbulence

The effect of island width on the multi-scale interactions between magnetic island (MI) and ion temperature gradient (ITG) turbulence has been investigated based on the global gyrokinetic approach[1]. It is found that the coupling between the island and turbulence is enhanced when the MI width (w) becomes larger[2,3]. A vortex flow whose amplitude depends sensitively on the island width, can be excited, which will finally lead to a strong  shear flow thus a decrease of the turbulence transport. The shearing rate induced by the vortex flow is minimum at the O-point while it is maximum at both of the two reconnection points of the island, i.e., the X-points, regardless of the island width. There exists a nonmonotonic relationship between zonal flow (ZF) amplitude and island width, showing that the ZF is partially suppressed by medium-sized MIs whereas enhanced in the case of large island. A larger MI can tremendously damage the ITG mode structure, resulting in higher turbulent transport at the X-point whereas a lower one at the O-point, respectively. Such phenomenon will be less distinct at very small island widths below w/a ~ 8% (a is the minor radius), where it shows that turbulence near the X-point is hardly affected although it is still suppressed inside the island. Furthermore, the influence of different island sizes on turbulence transport level is also discussed. [4]   

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We investigate the drift wave – zonal flow interaction mechanism in plasma edge turbulence using the recent two-field flux-balanced Hasegawa-Wakatani model, whose particularity is an improved treatment of the electron response on magnetic flux surfaces. A sharp transition is observed from a turbulence dominated regime to a zonal jet dominated regime. The robust zonal jets are further enhanced with multi-scale dynamics when the numerical domain is elongated in the radial direction. We analyze the generation and stability of the zonal state based on the selective decay principle and the secondary instability analysis. The generation of zonal jets is displayed from the secondary instability analysis via nonlinear interactions with a linearly unstable drift base mode, while stabilizing damping effect is shown from a zonal flow base state. The selective decay process can be characterized by transient visits to several metastable states, then final convergence to a purely zonal state. We rely on detailed statistical analysis of our numerical experiments to highlight the energy transfer mechanisms. The insights gained from investigating the properties of our simple model can lead to guidelines for the development of model reduction methods for more complicated systems.   

The impact of impurities and fast particles on STEP confinement

Multiple flux-tube gyrokinetic codes - GS2, CGYRO, GENE and GKW - applied to a high β~9% STEP flat top operating point reveal the presence of a dominant hybrid-KBM (coupled to a TEM) and a subdominant MTM. In these regimes, the inclusion of δB_∥ is critical to recovering the dominant instability [1].  Nonlinear flux-tube gyrokinetic simulations including only thermal components of the plasma, and neglecting equilibrium  flow-shear, indicate that the transport fluxes may be very large, but including equilibrium flow shear (at the level of the diamagnetic flow), reduces the heat flux considerably to a value that is more compatible with the assumed sources [2]. While this is encouraging, there is a large uncertainty on the flow shear value:  to bound this more accurately, it is important to include the missing physics.

It is seen that additional stabilization of hybrid KBMs is achieved, with a corresponding reduction in turbulent fluxes, when a self-consistent equilibrium that includes the fast-alpha pressure is considered. The inclusion of kinetic impurities (He, Ar, Xe) to the main ions has a further stabilizing impact. Finally, detailed studies of multiple STEP operating points (e.g. electron cyclotron vs electron Bernstein wave heated) which include the kinetic fast-alphas are underway, and we will report on these findings at the meeting.

[1] D. Kennedy et al, submitted to Nucl. Fusion

[2] M. Giacomin et al, submitted to Nucl. Fusion   

Collective Modes Associated with Rarefied Populations of Heavy Nuclei*

Plasmas in which low density populations of heavier nuclei than those of the main population are a frequent occurrence [1] and an important case is that of “impurities” whose cyclotron frequencies, Ω_I , differ from that, Ω_i, of the main population. “Ω_I- frequency” modes are found to be sustained by the impurity density gradient. In the limit of “short” transverse wavelengths (k^{2}d_{i}^{2}>1, where d_{i}=c/omega_{pi}) these modes are nearly electrostatic while in the relatively long wavelength limit (k^{2}d_{i}^{2}<< 1) they involve significant magnetic field fluctuations [2]. The relevant transverse phase velocities are in the direction of the local impurity diamagnetic velocity and produce a transport of this population across the magnetic field. Growth rates are found which depend on pre-existing thermal energy transport processes for the same population such as those associated with the excitation of the lower frequency “impurity drift modes” introduced in Ref. [3]. A programmed immission of non-reacting minority populations is suggested in order to increase the total reactivity of a fusion burning plasma column, for instance, by conditioning the spatial density profiles [1] of the reacting populations. *Sponsored in part by the Kavli Foundation (MIT and by ENEA (Italy).

[1] C. Mazzotta, et al., Paper IAEA-CN-899 MFE, Fusion Energy Conference (I.A.E.A., Vienna, 2021).

[2] B. Coppi, S. Cowley, et al., Phys. Fluids 29, 4060 (1986).

[3] B. Coppi, H. Furth, M. Rosenbluth and R. Sagdeev, Phys. Rev. Lett. 17, 377 (1966).